B3. Istanbul 2004 
ntrol points with 
'ound coordinates 
procedure we can 
€ gross error is. 
ination and solve 
nce we made the 
, our duty now to 
d finally we can 
d the gross error. 
an group them by 
„SP 23.45} 
S a gross error, it 
ong and only the 
by this logic we 
cause for a gross 
number of points 
ross-error is more 
1 is that finally at 
ain (otherwise no 
nt). 
Whether a space 
SS error or not: 
on center we can 
(13) 
weight unit error 
th the help of the 
(14) 
  
International Archives of the Photo 
STEP 3. The errors of (15) can be estimated before the 
adjustment by the following formulas: 
  
(16) 
STEP 4. The space resection is free from gross errors if 
m, sm, 
m sim, (17) 
m, S n, 
Otherwise we should setup a null- hypothesis to compare two 
RMS values (Detrekoi, 1991): : 
H o 330, (18) 
At p = 0.95% probality level with rank of freedom equal to 3, 
we get the statistical value as Borsa 
as a theoretical value and we symbolise it with F. On the 
— 928. Let's consider it 
other hand the value can be calculated by the following 
equations for each coordinate: 
  
  
  
  
  
  
2 
Es 2. 1 
M 80 o 232 
noe 3 
9 
my] (19) 
Sy ed 2 
E m 33 
2 
E cu. 1 
e an A25 re 22 
ip, 3. 
It means the space resection has no gross-error if the following 
equations will be fulfilled together: 
A JA 
Mo 
F. Y (20) 
E. 7 
IA 
DH 
Otherwise, we can deny the null-hypothesis and we should 
consider a gross-error in the space resection. 
grammetry, Remote Sensing and Spatial Information Sciences, Vol XXX V, Part B3. Istanbul 2004 
3. CONCLUSIONS 
3.1 Space resection 
Regarding the procedure of (1)-(6) we can notice that more than 
one solutions are probable for the projection center. If we have 
only three control points the maximally possible number of 
solutions is 8. Hence we get the tetrahedron sides from a forth- 
degree equation (3) and the equations of (6) will double it. Of 
course we will eliminate the complex and negative solutions, 
but still in this case we can get more than one solutions. So, to 
have a unique solution we need at least four control points, but 
in this case we should do the resection with an adjustment. 
3.2 Gross error detection 
The gross-error can be detected by formulas of (15)-(20) and 
even we can tell exactly which coordinate has a gross error. See 
the example in Appendix I. 
It still needs more investigation to determine the exact 
7 m s Sir ; 
PF matrix from a real partial derivation (9), which probably 
results more accurate and better based gross-error detection 
from theoretical point of view. 
REFERENCES 
References from Journals: 
Gleinsvik, P.:The generalisation of the theorem of Jacobi 
Buletin Geodesique , pp 269-280. 1967 
Jancso, T.:4 kulso tajekozasi elemek meghatarozasa kozvetlen 
analitikus modszerrel Geodezia es Kartografia, Budapest No. 
l. pp 33-38., 1994. 
References from Books: 
Detrekoi, A.: Kiegyenlito szamitasok, Tankonyvkiado, 
Budapest, pp. 74-75. 1991. 
References from Other Literature: 
Hirvonen, R.A.: General formulas for the analytical treatment 
of the problems of photogrammetry Suomen F otogrammetrinen 
Seura, Helsinki, Eripainos, Maamittans No: 3-4. 1964,